**A New Look at Electric Potential**

Induced electric fields are produced not by static charges but by a changing magnetic flux. Although electric fields produced in either way exert forces on charged particles. there is an important difference between them. The simplest evidence of this difference is that the field lines of induced electric fields form closed loops. as in. Field lines produced by static charges never do so but must start on ‘positive charges and end on negative charges.

Equation 31-27 gives the magnitude of the electric field at any point

for which r S R (that is, within the magnetic field). Subsututing

given values yields, for the magnitude of Eat r = 5.2 em,

E = (5.2 X 10-

2

m) (0.13 TIs)

2

= 0.0034 VIm = 3.4 mV/m. (Answer)

(b) Find an expr~on for the magnitude E of the induced electric

field at points that are outside the magnetic field. at radius r. Evaluate

the expression for r = 12.5 cm.

SOLUTION: The Key Idea of pan (a) applies here also. except that we

use a circular path of integration with radius r 2: R, because we

want to evaluate E for points outside the magnetic field. Proceeding

as in (a), we again obtain Eq. 31-25. However, we do not then

obtain Eq. 31-26, because the new path of integration i~ now outside

the magnetic field. and we need this Key Idea: The magnetic

flux encircled by the new path is only that in the area TrR2 of the

magnetic field region. Therefore.

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